On a perfectly smooth one orbit a small body moves under the influence of the constant gravity of the earth. The Guide way is in the "natural coordinates "s given by the equation: s ()= a In [1/ cose]. The movement of the body (point mass m) starts from rest at s=0. Determine the velocity of the body and the force acting between the body and the path Contact force N as a function of the angle o. Show that the path taken depends on time as follows s(t) = 2a. In[cosh (t 2a K d.